🧮 algebra

1. **State the problem:** Rationalise the denominator of $$\frac{6 + 5\sqrt{3}}{3 - 2\sqrt{3}}$$ and express the answer in the form $$a + b\sqrt{3}$$ where $$a$$ and $$b$$ are inte

1. The problem is to analyze the linear function $y=2x+1$. 2. This function is in slope-intercept form $y=mx+b$, where $m=2$ is the slope and $b=1$ is the y-intercept.

1. The problem asks to find all rectangles with natural number dimensions whose area is 72 square units, and then find their perimeters. We also need to determine when the perimete

1. The problem is to analyze the linear function $y=2x+1$. 2. This function is in slope-intercept form $y=mx+b$, where $m=2$ is the slope and $b=1$ is the y-intercept.

1. **State the problem:** We need to show two binomial coefficient identities: a) $\binom{n}{1} = n$

1. The problem is to find an equation for $x$. 2. To provide an equation for $x$, we need more information or context, such as an expression or relationship involving $x$.

1. The problem is to find the Least Common Multiple (LCM) of given numbers using prime factorization. 2. Prime factorization means breaking down each number into its prime factors.

1. The problem asks to find the constant value of either q1 or q2. 2. Since no specific equation or context is given, we assume q1 and q2 are constants.

1. **State the problem:** Solve the system of equations: $$9(9^x) = 27^{y+2}$$

1. **State the problem:** We are given the function $$y = (x+3)^2 + 2$$ and need to find the function's vertex and describe its graph. 2. **Identify the function type:** This is a

1. The problem is to understand the expansion of the function $$G(s) = s^{v-qr} \left[ 1 - \frac{a}{s^q} \right]^{-r}$$

1. The slope of a line measures how steep the line is. 2. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

1. The problem asks to estimate the number of CDs sold in 2006 based on the trend from 1999 to 2005 shown in a scatter plot. 2. Since the data shows a decreasing trend over time, a

1. **Problem:** Simplify the expression $\frac{1-3s-7}{1-s}$. 2. **Step 1:** Write the numerator clearly: $1 - 3s - 7 = (1 - 7) - 3s = -6 - 3s$.

1. **State the problem:** Factorise the quadratic expression $15x^2 - 16x - 15$. 2. **Identify coefficients:** Here, $a = 15$, $b = -16$, and $c = -15$.

1. The problem is to solve the quadratic equation $$2x^2 - 4x - 6 = 0$$. 2. First, identify the coefficients: $$a = 2$$, $$b = -4$$, and $$c = -6$$.

1. The problem is to solve the quadratic equation $$2x^2 - 4x - 6 = 0$$. 2. First, identify the coefficients: $$a = 2$$, $$b = -4$$, and $$c = -6$$.

1. The problem is to solve the equation $$2x + 3 = 11$$ for $x$. 2. Start by isolating the variable term on one side. Subtract 3 from both sides:

1. **State the problem:** We are given total Covid-19 cases in Egypt on two dates: July 24, 2020 (91,072 cases) and August 3, 2020 (94,640 cases). We assume the number of cases cha

1. The problem is to evaluate the square root of 3, written as $\sqrt{3}$.\n\n2. The square root function $\sqrt{x}$ gives the number which, when multiplied by itself, equals $x$.\

1. **State the problem:** We have two lines given by equations: $$2x + ty = -1$$